E - Finite Encyclopedia of Integer Sequences

Time Limit: 2 sec / Memory Limit: 256 MB

制約

• 1 \leq K,N \leq 3 × 10^5
• N,K は整数である

入力

K N


入力例 1

3 2


出力例 1

2 1


入力例 2

2 4


出力例 2

1 2 2 2


入力例 3

5 14


出力例 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2


Score : 800 points

Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.

Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

• 1 \leq N,K \leq 3 × 10^5
• N and K are integers.

Input

Input is given from Standard Input in the following format:

K N


Output

Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

Sample Input 1

3 2


Sample Output 1

2 1


There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3). The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

Sample Input 2

2 4


Sample Output 2

1 2 2 2


Sample Input 3

5 14


Sample Output 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2